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Quantum Mechanics in Chemistry

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Quantum Mechanics in Chemistry

This is a text dealing with the basics of quantum mechanics and electronic structure theory. It provides an introduction to molecular spectroscopy and to the subject of molecular dynamics.

Physical and Theoretical Chemistry Textbook MapsChemistry
Author
Jack Simons and Jeff Nichols
Publisher
University of Utah
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 153 sections
  1. 01: The Basic Tools of Quantum Mechanics
  2. 1.01: Operators
  3. 1.02: Wavefunctions
  4. 1.03: The Schrodinger Equation
  5. 1.04: Free-Particle Motion in Two Dimensions
  6. 1.05: Particles in Boxes
  7. 1.06: One Electron Moving About a Nucleus
  8. 1.07: Harmonic Vibrational Motion
  9. 1.08: Rotational Motion for a Rigid Diatomic Molecule
  10. 1.09: The Physical Relevance of Wavefunctions Operators and Eigenvalues
  11. 02: Approximation Methods
  12. 2.0E: 2.E: Approximation Methods (Exercises)
  13. 2.01: The Variational Method
  14. 2.02: Perturbation Theory
  15. 03: Nuclear Motion
  16. 3.0E: 3.E: Exercises
  17. 3.01: The Born-Oppenheimer Separation of Electronic and Nuclear Motions
  18. 3.02: Time Scale Separation
  19. Rotation States for Each Electronic Surface
  20. 3.04: Rotation and Vibration of Diatomic Molecules
  21. 3.05: Separation of Vibration and Rotation
  22. 3.06: The Rigid Rotor and Harmonic Oscillator
  23. 3.07: The Morse Oscillator
  24. 3.08: Rotation of Polyatomic Molecules
  25. 3.09: Rotation of Linear Molecules
  26. 3.10: Rotation of Non-Linear Molecules
  27. 3.11: Chapter Summary
  28. 04: Atomic Orbitals
  29. 4.01: Shapes of Atomic Orbitals
  30. 4.02: Directions of Atomic Orbitals
  31. 4.03: Sizes and Energies
  32. 05: Molecular Orbitals
  33. 5.01: Orbital Interaction Topology
  34. 5.02: Orbital Symmetry
  35. 5.03: Linear Molecules
  36. 5.04: Atoms
  37. 06: Quantum Mechanics in Reactions
  38. 6.01: Reduction in Symmetry Along Reaction Paths
  39. 6.02: Orbital Correlation Diagrams - Origins of the Woodward-Hoffmann Rules
  40. 07: Further Characterization of Molecular Orbitals
  41. 7.01: The LCAO-MO Expansion and the Orbital-Level Schrödinger Equation
  42. 7.02: Determining the Effective Potential
  43. 7.03: The Hückel Parameterization
  44. 7.04: The Extended Hückel Method
  45. 08: Electronic Configurations
  46. 8.01: Orbitals Do Not Provide the Complete Picture; Their Occupancy By the N Electrons Must Be Specified
  47. 8.02: Even N-Electron Configurations are Not Mother Nature's True Energy States
  48. 8.03: Mean-Field Models
  49. 8.04: Configuration Interaction (CI) Describes the Correct Electronic States
  50. 8.05: Summary
  51. 09: Symmetry of Electronic Wavefunctions
  52. 9.01: Electronic Configurations
  53. 9.02: Antisymmetric Wavefunctions
  54. 10: Angular Momentum and Group Symmetries of Electronic Wavefunctions
  55. 10.01: Angular Momentum Symmetry and Strategies for Angular Momentum Coupling
  56. 10.02: Electron Spin Angular Momentum
  57. 10.03: Coupling of Angular Momenta
  58. 10.04: Atomic Term Symbols and Wavefunctions
  59. 10.05: Atomic Configuration Wavefunctions
  60. 10.06: Inversion Symmetry
  61. 10.07: Review of Atomic Cases
  62. 11: Evaluating the Matrix Elements of N-electron Wavefunctions
  63. 11.0S: 11.S: Evaluating the Matrix Elements of N-electron Wavefunctions (Summary)
  64. 11.01: Configuration State Functions can Express the Full N-Electron Wavefunction
  65. 11.02: The Slater-Condon Rules Give Expressions for the Operator Matrix Elements Among the CSFs
  66. 11.03: The Slater-Condon Rules
  67. 11.04: Examples of Applying the Slater-Condon Rules
  68. 12: Quantum Mechanical Picture of Bond Making and Breaking Reactions
  69. 12.01: Concepts of Configuration and State Energies
  70. 12.02: Mixing of Covalent and Ionic Configurations
  71. 12.03: Various Types of Configuration Mixing
  72. 13: Molecular Rotation and Vibration
  73. 13.01: Rotational Motions of Rigid Molecules
  74. 13.02: Vibrational Motion Within the Harmonic Approximation
  75. 13.03: Anharmonicity
  76. 14: Time-dependent Quantum Dynamics
  77. 14.01: Time-Dependent Vector Potentials
  78. 14.02: Time-Dependent Perturbation Theory
  79. 14.03: Application to Electromagnetic Perturbations
  80. 14.04: The "Long-Wavelength" Approximation
  81. 14.05: The Kinetics of Photon Absorption and Emission
  82. 15: Spectroscopy
  83. 15.01: Rotational Transitions
  84. 15.02: Vibration-Rotation Transitions
  85. 15.03: Electronic-Vibration-Rotation Transitions
  86. 15.04: Time Correlation Function Expressions for Transition Rates
  87. 16: Collisions and Scattering
  88. 16.01: One Dimensional Scattering
  89. 16.02: Multichannel Problems
  90. 16.03: Classical Treatment of Nuclear Motion
  91. 16.04: Wavepackets
  92. 17: Higher Order Corrections to Electronic Structure
  93. 17.01: Orbitals, Configurations, and the Mean-Field Potential
  94. 17.02: Electron Correlation Requires Moving Beyond a Mean-Field Model
  95. 17.03: Moving from Qualitative to Quantitative Models
  96. 17.04: Atomic Units
  97. 18: Multiconfiguration Wavefunctions
  98. 18.01: Optimization of the Energy for a Multiconfiguration Wavefunction
  99. 18.02: The Single-Determinant Wavefunction
  100. 18.03: The Unrestricted Hartree-Fock Spin Impurity Problem
  101. 18.04: Atomic Orbital Basis Sets
  102. 18.05: The LCAO-MO Expansion
  103. 18.06: The Roothaan Matrix SCF Process
  104. 18.07: Observations on Orbitals and Orbital Energies
  105. 19: Multi-Determinant Wavefunctions
  106. 19.01: Introduction to Multi-Determinant Wavefunctions
  107. 19.02: Different Methods
  108. 19.03: Strengths and Weaknesses of Various Methods
  109. 19.04: Further Details on Implementing Multiconfigurational Methods
  110. 20: Response Theory
  111. 20.01: Calculations of Properties Other Than the Energy
  112. 20.02: Ab Initio, Semi-Empirical, and Empirical Force Field Methods
  113. 21: Problem Sets
  114. 22: Problems
  115. 22.01: The Basic Tools of Quantum Mechanics
  116. 22.1.01: i. Review Exercises
  117. 22.1.02: ii. Exercises
  118. 22.1.03: iii. Problems 1-10
  119. 22.1.04: iv. Problems 11-18
  120. 22.1.05: v. Review Exercise Solutions
  121. 22.1.06: vi. Exercise Solutions
  122. 22.02: Simple Molecular Orbital Theory
  123. 22.2.01: i. Review Exercises
  124. 22.2.02: ii. Exercises
  125. 22.2.03: iii. Problems
  126. 22.2.04: iv. Review Exercises Solutions
  127. 22.2.05: v. Exercise Solution
  128. 22.2.06: vi. Problem Solutions
  129. 22.03: Electronic Configurations, Term Symbols, and States
  130. 22.3.01: i. Review Exercises
  131. 22.3.02: ii. Exercises
  132. 22.3.03: iii. Problems
  133. 22.3.04: iv. Review Exercise Solutions
  134. 22.3.05: v. Exercise Solutions
  135. 22.3.06: vi. Problem Solutions
  136. 22.04: Molecular Rotation and Vibration
  137. 22.4.01: i. Exercises
  138. 22.4.02: ii. Problems
  139. 22.4.03: iii. Exercise Solutions
  140. 22.4.04: iv. Problem Solutions
  141. 22.05: Time Dependent Processes
  142. 22.5.01: i. Exercises
  143. 22.5.02: ii. Problems
  144. 22.5.03: iii. Exercise Solutions
  145. 22.5.04: iv. Problem Solutions
  146. 22.06: More Quantitative Aspects of Electronic Structure Calculations
  147. 22.6.01: i. Review Execises
  148. 22.6.02: i. Review Exercises-
  149. 22.6.03: ii. Exercises
  150. 22.6.04: iii. Problems
  151. 22.6.05: iv. Review Exercise Solutions
  152. 22.6.06: v. Exercise Solutions
  153. 22.6.07: vi. Problem Solutions